Question: $9tu - 9tv + 10t + 5 = -3u - 9$ Solve for $t$.
Solution: Combine constant terms on the right. $9tu - 9tv + 10t + {5} = -3u - {9}$ $9tu - 9tv + 10t = -3u - {14}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $9{t}u - 9{t}v + 10{t} = -3u - 14$ Factor out the $t$ ${t} \cdot \left( 9u - 9v + 10 \right) = -3u - 14$ Isolate the $t$ $t \cdot \left( {9u - 9v + 10} \right) = -3u - 14$ $t = \dfrac{ -3u - 14 }{ {9u - 9v + 10} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{3u + 14}{-9u + 9v - 10}$